Notes on math, coding, and other stuff

Tag: english

I was born in China and immigrated to Canada when I was 4 years old. After living in Canada for 18 years, I consider myself a native speaker for most purposes, but I still retain a noticeable non-native accent when speaking.

This post has a video that contains me speaking, if you want to hear what my accent sounds like.

It’s often considered very difficult or impossible to change your accent once you reach adulthood. I don’t know if this is true or not, but it sounds like a self-fulfilling prophecy — the more you think it’s impossible, the less you try, so of course your accent will not get any better. Impossible or not, it’s worth it to give it a try.

The first step is identifying what errors you’re making. This can be quite difficult if you’re not a trained linguist — native English speakers will detect that you have an accent, but they can’t really pinpoint exactly what’s wrong with your speech — it just sounds wrong to them.

One accent reduction strategy is the following: listen to a native speaker saying a sentence (for example, in a movie or on the radio), and repeat the same sentence, mimicking the intonation as closely as possible. Record both sentences, and play them side by side. This way, with all the other confounding factors gone, it’s much easier to identify the differences between your pronunciation and the native one.

When I tried doing this using Audacity, I noticed something interesting. Oftentimes, it was easier to spot differences in the waveform plot (that Audacity shows automatically) than to hear the differences between the audio samples. When you’re used to speaking a certain way all your life, your ears “tune out” the differences.

Here’s an example. The phrase is “figure out how to sell it for less” (Soundcloud):

The difference is clear in the waveform plot. In my audio sample, there are two spikes corresponding to the “t” sound that don’t appear in the native speaker’s sample.

For vowels, the spectrogram works better than the waveform plot. Here’s the words “said” and “sad”, which differ in only the vowel:

Again, if you find it difficult to hear the difference, it helps to have a visual representation to look at.

I was surprised to find out that I’d been pronouncing the “t” consonant incorrectly all my life. In English, the letter “t” represents an aspirated alveolar stop (IPA /tʰ/), which is what I’m doing, right? Well, no. The letter “t” does produce the sound /tʰ/ at the beginning of a word, but in American English, the “t” at the final position of a word can get de-aspirated so that there’s no audible release. It can also turn into a glottal stop (IPA /ʔ/) in some dialects, but native speakers rarely pronounce /tʰ/, except in careful speech.

This is a phonological rule, and there are many instances of this. Here’s a simple experiment: put your hand in front of your mouth and say the word “pin”. You should feel a puff of air in your palm. Now say the word “spin” — and there is no puff of air. This is because in English, the /p/ sound always changes into /b/ following the /s/ sound.

Now this got me curious and I wondered: exactly what are the rules governing sound changes in English consonants? Can I learn them so I don’t make this mistake again? Native English speakers don’t know these rules (consciously at least), and even ESL materials don’t go into much detail about subtle aspects of pronunciation. The best resources for this would be linguistics textbooks on English phonology.

I consulted a textbook called “Gimson’s Pronunciation of English” [1]. For just the rules regarding sound changes of the /t/ sound at the word-final position, the book lists 6 rules. Here’s a summary of the first 3:

No audible release in syllable-final positions, especially before a pause. Examples: mat, map, robe, road. To distinguish /t/ from /d/, the preceding vowel is lengthened for /d/ and shortened for /t/.

In stop clusters like “white post” (t + p) or “good boy” (d + b), there is no audible release for the first consonant.

When a plosive consonant is followed by a nasal consonant that is homorganic (articulated in the same place), then the air is released out of the nose instead of the mouth (eg: topmost, submerge). However, this doesn’t happen if the nasal consonant is articulated in a different place (eg: big man, cheap nuts).

As you can see, the rules are quite complicated. The book is somewhat challenging for non-linguists — these are just the rules for /t/ at the word-final position; the book goes on to spend hundreds of pages to cover all kinds of vowel changes that occur in stressed and unstressed syllables, when combined with other words, and so on. For a summary, take a look at the Wikipedia article on English Phonology.

What’s really amazing is how native speakers learn all these patterns, perfectly, as babies. Native speakers may make orthographic mistakes like mixing up “their, they’re, there”, but they never make phonological mistakes like forgetting to de-aspirate the /p/ in “spin” — they simply get it right every time, without even realizing it!

Some of my friends immigrated to Canada at a similar or later age than me, and learned English with no noticeable accent. Therefore, people sometimes found it strange that I still have an accent. Even more interesting is the fact that although my pronunciation is non-native, I don’t make non-native grammatical mistakes. In other words, I can intuitively judge which sentences are grammatical or ungrammatical just as well as a native speaker. Does that make me a linguistic anomaly? Intrigued, I dug deeper into academic research.

In 1999, Flege et al. conducted a study of Korean-American immigrants who moved to the USA at an early age [2]. Each participant was given two tasks. In the first task, the participant was asked to speak a series of English sentences, and native speakers judged how much of a foreign accent was present on a scale from 1 to 9. In the second task, the participant was a list of English sentences, some grammatical and some not, and picked which ones were grammatical.

Linguists hypothesize that during first language acquisition, babies learn the phonology of their language long before they start to speak; grammatical structure is acquired much later. The Korean-American study seems to support this hypothesis. For the phonological task, immigrants who arrived as young as age 3 sometimes retained a non-native accent into adulthood.

Above: Scores for phonological task decrease as age of arrival increases, but even very early arrivals retain a non-native accent.

Basically, arriving before age 6 or so increases the chance of the child developing a native-like accent, but by no means does it guarantee it.

On the other hand, the window for learning grammar is much longer:

Above: Scores for grammatical task only start to decrease after about age 7.

Age of arrival is a large factor, but does not explain everything. Some people are just naturally better at acquiring languages than others. The study also looked at the effect of other factors like musical ability and perceived importance of English on the phonological score, but the connection is a lot weaker.

Language is so easy that every baby picks it up, yet so complex that linguists write hundreds of pages to describe it. Even today, language acquisition is poorly understood, and there are many unresolved questions about how it works.

I’m an avid language learner, and sometimes people ask me: “how many languages do you speak?” If we’re counting all the languages in which I can have at least a basic conversation, then I can speak five languages — but can I really claim fluency in a language if I can barely read children’s books? Despite being a seemingly innocuous question, it’s not so simple to answer. In this article, I’ll try to explain why.

Let’s say you’re just starting to study Japanese. You might picture yourself being able to do the following things, after a few months or years of study:

Have a conversation with a Japanese person who doesn’t speak any English

Watch the latest episode of some anime in Japanese before the English subtitles come out

Overhear a conversation between two Japanese people in an elevator

After learning several languages, I discovered that the first task is a lot easier than the other two, by an order of magnitude. Whether in French or in Japanese, I would quickly learn enough of the language to talk to people, but the ability to understand movies and radio remains elusive even after years of study.

There is a fundamental difference in how language is used in one-on-one conversation versus the other two tasks. When conversing with a native speaker, it is possible for him to avoid colloquialisms, speak slower, and repeat things you didn’t understand using simpler words. On the other hand, when listening to native-level speech without the speaker adjusting for your language level, you need to be near native-level yourself to understand what’s going on.

We can justify this concept using statistics. By looking at how frequencies of English words are distributed, we show that after an initial period of rapid progress, it soon becomes exponentially harder to get better at a language. Conversely, even a small decrease in language complexity can drastically increase comprehension by non-native listeners.

Reaching conversational level is easy

For the rest of this article, I’ll avoid using the word “fluent”, which is rather vague and misleading. Instead, I will call a “conversational” speaker someone who can conduct some level of conversation in a language, and a “near-native” speaker someone who can readily understand speech and media intended for native speakers.

It’s surprising how little of a language you actually need to know to have a decent conversation with someone. Basically, you need to know:

A set of about 1000-2000 very basic words (eg: person, happy, cat, slow, etc).

Enough grammar to form sentences (eg: present / future / past tenses; connecting words like “then”, “because”; conditionals, comparisons, etc). Grammar doesn’t need to be perfect, just close enough for the listener to understand what you’re trying to say.

When you want to say something but don’t know the word for it, be flexible enough to work around the issue and express it with words you do know.

For another example, imagine that Bob, a native English speaker, is talking to Jing, an international student from China. Their conversation might go like this:

Bob: I read in the news that a baby got abducted by wolves yesterday…

Jing: Abducted? What do you mean?

Bob: He got taken away by wolves while the family was out camping.

Jing: Wow, that’s terrible! Is he okay now?

In this conversation, Jing indicates that she doesn’t understand a complex word, “abducted”, and Bob rephrases the idea using simpler words, and the conversation goes on. This pattern happens a lot when I’m conversing with native Japanese speakers.

After some time, Bob gets an intuitive feeling for what level of words Jing can understand, and naturally simplifies his speech to accommodate. This way, the two can converse without Jing explicitly interrupting and asking Bob to repeat what he said.

Consequently, reaching conversational level in a language is not very hard. Some people claim you can achieve “fluency” in 3 months for a language. I think this is a reasonable amount of time for reaching conversational level.

What if you don’t have the luxury of the speaker simplifying his level of speech for you? We shall see that the task becomes much harder.

The curse of the Power Law

Initially, I was inspired to write this article after an experience with a group of French speakers. I could talk to any of them individually in French, which is hardly remarkable given that I studied the language since grade 4 and minored in it in university. However, when they talked between themselves, I was completely lost, and could only get a vague sense of what they were talking about.

Feeling slightly embarrassed, I sought an explanation for this phenomenon. Why was it that I could produce 20-page essays for university French classes, but struggled to understand dialogue in French movies and everyday conversations between French people?

The answer lies in the distribution of word frequencies in language. It doesn’t matter if you’re looking at English or French or Japanese — every natural language follows a power law distribution, which means that the frequency of every word is inversely proportional to its rank in the frequency table. In other words, the 1000th most common word appears twice as often as the 2000th most common word, and four times as often as the 4000th most common word, and so on.

(Aside: this phenomenon is sometimes called Zipf’s Law, but refers to the same thing. It’s unclear why this occurs, but the law holds in every natural language)

Above: Power law distribution in natural languages

The power law distribution exhibits the long tail property, meaning that as you advance further to the right of the distribution (by learning more vocabulary), the words become less and less common, but never drops off completely. Furthermore, rare words like “constitution” or “fallacy” convey disproportionately more meaning than common words like “the” or “you”.

This is bad news for language learners. Even if you understand 90% of the words of a text, the remaining 10% are the most important words in the passage, so you actually understand much less than 90% of the meaning. Moreover, it takes exponentially more vocabulary and effort to understand 95% or 98% or 99% of the words in the text.

I set out to experimentally test this phenomenon in English. I took the Brown Corpus, containing a million words of various English text, and computed the size of vocabulary you would need to understand 50%, 80%, 90%, 95%, 98%, 99%, and 99.5% of the words in the corpus.

By knowing 75 words, you already understand half of the words in a text! Of course, just knowing words like “the” and “it” doesn’t get you very far. Learning 2000 words is enough to have a decent conversation and understand 80% of the words in a text. However, it gets exponentially harder after that: to get from 80% to 98% comprehension, you need to learn more than 10 times as many words!

(Aside: in this analysis I’m considering conjugations like “swim” and “swimming” to be different words; if you count only the stems, you end up with lower word counts but they still follow a similar distribution)

How many words can you miss and still be able to figure out the meaning by inference? In a typical English novel, I encounter about one word per page that I’m unsure of, and a page contains about 200-250 words, so I estimate 99.5% comprehension is native level. When there are more than 5 words per page that I don’t know, then reading becomes very slow and difficult — this is about 98% comprehension.

Therefore I will consider 98% comprehension “near-native”: above this level, you can generally infer the remaining words from context. Below this level, say between 90% to 98% comprehension, you may understand generally what’s going on, but miss a lot of crucial details.

Above: Perceived learning curve for a foreign language

This explains the difficulty of language learning. In the beginning, progress is fast, and in a short period of time you learn enough words to have conversations. After that, you reach a long intermediate-stage plateau where you’re learning more words, but don’t know enough to understand native-level speech, and anybody speaking to you must use a reduced vocabulary in order for you to understand. Eventually, you will know enough words to infer the rest from context, but you need a lot of work to reach this stage.

Implications for language learners

The good news is that if you want to converse with people in a language, it’s perfectly doable in 3 to 6 months. On the other hand, to watch TV shows in the language without subtitles or understand people speaking naturally is going to take a lot more work — probably living for a few years in a country where the language is spoken.

Is there any shortcut instead of slowly learning thousands of words? I can’t say for sure, but somehow I doubt it. By nature, words are arbitrary clusters of sounds, so no amount of cleverness can help you deduce the meaning of words you’ve never seen before. And when the proportion of unknown words is above a certain threshold, it quickly becomes infeasible to try to infer meaning from context. We’ve reached the barrier imposed by the power law distribution.

Now I will briefly engage in some sociological speculation.

My university has a lot of international students. I’ve always noticed that these students tend to form social groups speaking their native non-English languages, and rarely assimilate into English-speaking social groups. At first I thought maybe this was because their English was bad — but I talked to a lot of international students in English and their English seemed okay: noticeably non-native but I didn’t feel there was a language barrier. After all, all our lectures are in English, and they get by.

However, I noticed that when I talked to international students, I subconsciously matched their rate of speaking, speaking just a little bit slower and clearer than normal. I would also avoid the usage of colloquialisms and cultural references that they might not understand.

If the same international student went out to a bar with a group of native English speakers, everyone else would be speaking at normal native speed. Even though she understands more than 90% of the words being spoken, it’s not quite enough to follow the discussion, and she doesn’t want to interrupt the conversation to clarify a word. As everything builds on what was previously said in the conversation, missing a word here and there means she is totally lost.

It’s not that immigrants don’t want to assimilate into our culture, but rather, we don’t realize how hard it is to master a language. On the surface, going from 90% to 98% comprehension looks like a small increase, but in reality, it takes an immense amount of work.